Chapter 9.1, Problem 24WE

To determine

To calculate: Find the coordinates.

Answer to Problem 24WE

The coordinates of point Q are $\left(2h,2k\right)$ .

Explanation of Solution

Given information: The coordinates of two points P and M are $\left(0,0\right)$ and $\left(h,k\right)$ respectively.

Formula used: $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Calculation:

Two given points are $P\left(0,0\right)andM\left(h,k\right)$ .

Assume $\left(x,y\right)$ as the coordinates of Q,

Hence,

  $\begin{array}{l}\left(\frac{0+x}{2},\frac{0+y}{2}\right)=\left(h,k\right)\\ \Rightarrow \frac{0+x}{2}=h\\ \Rightarrow 0+x=2h\\ \therefore x=2h\end{array}$

Now, get the value of y,

  $\begin{array}{l}\Rightarrow \frac{0+y}{2}=k\\ \Rightarrow 0+y=2k\\ \therefore y=2k\end{array}$

Therefore, the coordinates of point Q are $\left(2h,2k\right)$ .